Abstract
In the present paper, we focus on the reducibility of an almost-periodic linear Hamiltonian system dX dt = J[A + epsilon Q(t)]X, X is an element of R2d, where J is an anti-symmetric symplectic matrix, A is a symmetric matrix, Q(t) is an analytic almost -periodic matrix with respect to t, and epsilon is a parameter which is sufficiently small. Using some non -resonant and non-degeneracy conditions, rapidly convergent methods prove that, for most sufficiently small epsilon, the Hamiltonian system is reducible to a constant coefficients Hamiltonian system through an almost-periodic symplectic transformation with similar frequencies as Q(t). At the end, an application to Schro center dot dinger equation is given.